3D Shock Transitions

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• A₁A₃-II: lower down the plane until the two red axial curves merge

• A₁²A₃-I: increase the bump at the A₁³ axial.

• A₁²A₃-II: lower down the bump until the tab hits the A₁³ axial.

• A₁A₃-I: http://www.lems.brown.edu/vision/researchAreas/Shocks3D/Results/3dTrans/A1A3_I_Bump.html
   

• A₁⁵: http://www.lems.brown.edu/vision/researchAreas/Shocks3D/Results/BlockCut.html
   

• A₁⁴: http://www.lems.brown.edu/vision/researchAreas/Shocks3D/Results/SqueezedTube.html
   

• A₁⁴: second example: increase height of the squeezed tube

   

• A₅: increase size of the bump and move it upward (to perturb the rib)

   

   

• Bogaevski, 26 types of perestroikas.

The 26 topologically different perestroikas of the momentary shock waves are shown by arrows (after Bogaevski).
Those relevant to the Medial Axis are indicated by a double-arrow.
Single lines indicate the (exterior) boundary of the shock illustration.
Double lines indicate rims where shock sheets are limited by surface ridges, i.e., they correspond to A_3 shock curves.
Triple lines indicate intercepts of shock sheets, i.e., they correspond to A_1^3 shock curves.
Concentric circles indicate an overlap of medial points.